Q: Which of the following best describes the end behavior of the polynomial $$f(x) = -2x^4$ + 3x^2$ - 5$$?

As $$x \to \infty$$, $$f(x) \to -\infty$$; as $$x \to -\infty$$, $$f(x) \to -\infty$$

Question 1

Which of the following best describes the main purpose of College Algebra as outlined in the syllabus?

Accepted Answer

To help students acquire a solid foundation in algebra, preparing them for other courses and real-world problem solving.

Question 2

A student is modeling the population growth of a bacteria culture using an exponential function. Which type of equation should they use?

Accepted Answer

$$y = ab^x$$

Question 3

Which of the following is NOT a function type specifically mentioned in the course syllabus for study in College Algebra?

Accepted Answer

Trigonometric

Question 4

If a student wants to solve the equation $$2x^2 - 8 = 0$, which algebraic technique should they use?

Accepted Answer

Isolate $$x by $$adding 8 to both sides, then dividing by 2, and finally taking the square root.

Question 5

A real-world scenario: A car's value depreciates by 15% each year. Which function best models the car's value $$V$$ after $$t$$ years if the initial value is $$V_0$$?

Accepted Answer

$$V = V_0$(0.85)^t$$

Question 6

Which of the following is a correct interpretation of the average rate of change of a function $$f(x)$$ between $$x = a$$ and $$x = b$$?

Accepted Answer

$$\frac{f(b) - f(a)}{b - a}$$

Question 7

A student is asked to solve the system of equations: $$\begin{cases} 2x + 3y = 7 \ x - y = 1 \end{cases}. $$What is the value of $$x$$?

Accepted Answer

$$x = 2$$

Question 8

Which of the following best describes a one-to-one function?

Accepted Answer

Each input has exactly one output, and each output has exactly one input.

Question 9

Given the function $$f(x) = x^2$, which of the following statements is true?

Accepted Answer

$$f(x) is an $$even function.

Question 10

A student is analyzing the graph of $$f(x) = \frac{1}{x}. $$Which of the following statements about its asymptotes is correct?

Accepted Answer

It has a vertical asymptote at $$x = 0$$ and a horizontal asymptote at $$y = 0.$$

Question 11

Which of the following is the correct formula for the sum of the first $$n$$ terms of an arithmetic sequence with first term $$a_1$$ and common difference $$d$$?

Accepted Answer

$$S_n = \frac{n}{2}(2a_1 + (n-1)d)$$

Question 12

A student is asked to solve the inequality $$|2x - 3| \u003c 5. $$Which of the following is the correct solution set?

Accepted Answer

$$-1 \u003c x \u003c 4$$

Question 13

Which of the following best describes the end behavior of the polynomial $$f(x) = -2x^4$ + 3x^2$ - 5$$?

Accepted Answer

As $$x 	o \infty$$, $$f(x) 	o -\infty$$; as $$x 	o -\infty$$, $$f(x) 	o -\infty$$

Question 14

A medical researcher uses the function $$P(t) = 1000e$$^{0.03t}$$ to model the growth of a bacteria population, where t$ is in hours. What is the initial population?

Accepted Answer

$$1000$$

Question 15

Which of the following is the correct inverse of the function $$f(x) = 3x + 7$$?

Accepted Answer

$$f^{-1}(x$$) = \frac{x - 7}{3}$$

Question 16

A student is asked to graph the piecewise function $$f(x) = \begin{cases} x + 2 & x \u003c 0 \ 2x - 1 & x \geq 0 \end{cases}. $$What is the value of $$f(0)$$?

Accepted Answer

$$-1$$

Question 17

Which of the following is the correct solution to the logarithmic equation $$\log_2$(x) = 5$$?

Accepted Answer

$$x = 32$$

Question 18

A student is given the function $$f(x) = \sqrt{x - 4}. $$What is the domain of $$f(x)$$?

Accepted Answer

$$x \geq 4$$

Question 19

Which of the following best describes the transformation applied to the graph of $$y = x^2$ to obtain y = (x$$ - $$3)^2 + 2$?

Accepted Answer

Shift right 3 units and up 2 units.

College Algebra Syllabus and Course Structure – MATH 1513

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